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Question

Draw 'less than' as well as 'more than' ogives for the following data: Weight (in Kg) 30−34 35−39 40−44 45−49 50−54 55−59 60−64 Frequency 3 5 12 18 14 6 2

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Solution

Before proceeding to construct the ogives, we first need to convert the given inclusive series into an exclusive series using the following formula. The value of adjustment as calculated is then added to the upper limit of each class and subtracted from the lower limit of each class. $\mathrm{Here},\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{adjustment}=\frac{35-34}{2}=0.5$ Therefore, we add 0.5 to the upper limit and subtract 0.5 from the lower limit of each class. Weight Frequency 29.5 − 34.5 34.5 − 39.5 39.5 − 44.5 44.5 − 49.5 49.5 − 54.5 54.5 − 59.5 59.5 − 64.5 3 5 12 18 14 6 2 Now for constructing a less than ogive, we convert the frequency distribution into a less than cumulative frequency distribution as follows. Weight Cumulative Frequency Less than 34.5 Less than 39.5 Less than 44.5 Less than 49.5 Less than 54.5 Less than 59.5 Less than 64.5 3 3 + 5 = 8 8 + 12 = 20 20 + 18 = 38 38 + 14 = 52 52 + 6 = 58 58 + 2 = 60 We now plot the cumulative frequencies against the upper limit of the class intervals. The curve obtained on joining the points so plotted is known as the less than ogive. For constructing a more than ogive, we convert the frequency distribution into a more than cumulative frequency distribution as follows. Weight Cumulative Frequency More than 0 More than 34.5 More than 39.5 More than 44.5 More than 49.5 More than 54.5 More than 59.5 More than 64.5 60 60 − 3 = 57 57 − 5 = 52 52 − 12 = 40 40 − 18 = 22 22 − 14 = 8 8 − 6 = 2 2 − 2 = 0 We now plot the cumulative frequencies against the lower limit of the class intervals. The curve obtained on joining the points so plotted is known as the more than ogive.

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